Slater's nonlocal exchange potential and beyond

Abstract

The local density approximation (LDA) to the exchange potential V x(r), namely the ρ1/3 electron gas form, was already transcended in Slater's 1951 paper. Here, using Dirac's 1930 form for the exchange energy density ∈x(r), the Slater (Sl) nonlocal exchange potential Vxsl(r) is defined by 2∈x(r)/ ρ(r). In spherical atomic ions, say the Be or Ne-like series, this form Vxsl(r) already has the correct behavior in both r → 0 and r → ∞ limits when known properties of the exchange energy density ∈x(r) and the ground-state electron density ρ(r) are invoked. As examples, some emphasis will first be given to the use of the so-called 1/Z expansion in such spherical atomic ions, for which analytic results can be obtained for both ∈x(r) and ρ(r) as the atomic number Z becomes large. The usefulness of the 1/Z expansion is directly demonstrated for the U atomic ion with 18 electrons by comparison with the optimized effective potential prediction. A rather general integral equation for the exchange potential is then proposed. Finally, without appeal to large Z, two-level systems are considered, with specific reference to the Be atom and to the LiH molecule. In all cases treated, the Slater potential Vxsl(r) is a valuable starting point, even though it needs apprecicorrections reflecting directly atomic shell structure. © 2004 Wiley Periodicals, Inc.